Related papers: Universal neural field computation
The emergence of classical behavior from quantum mechanics as Planck's constant $\hbar$ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly…
We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by…
In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system:…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Multimodal image alignment involves finding spatial correspondences between volumes varying in appearance and structure. Automated alignment methods are often based on local optimization that can be highly sensitive to their initialization.…
We introduce a novel tableau-based classical simulation method for quantum computation, formulated within the phase space framework of the extended stabilizer theory of closed non-contextual operators. This method enables the efficient…
Recent analyses of backward meson electroproduction support the validity of a collinear QCD factorization framework for these hard exclusive reactions. This opens a way to the extraction of nucleon-to-meson transition distribution…
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…
Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Alan Turing has never been considered to have approached a definition of Cellular Automata.…
Universal features of chaotic quantum dynamics underlie our understanding of thermalization in closed quantum systems and the complexity of quantum computations. Reversible automaton circuits, comprised of classical logic gates, have…
Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region.…
Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…